You have a square piece of paper and you do not know its length or width.
What is the minimum number of folds required in order for the paper to only show 1/15 of its original size, 2/15 of it's original size, 3/15 of its original size, ........, 14/15 of its original size.
Note: You do not know where onethird marks or onefifth marks lie on this piece of paper therefore you must use folds to mark these areas. You are allowed to use folds as guides to make other folds.
Part 1  creating 15 equal areasCrease square ABCD along diagonal BD.
A f4 f3 f2 f1 B
s1
t2
o
t1
q1
D C
Then fold into 4 quarters horizontally.
q1 is the intersection of BD with the lower quarter fold.
Crease along Cq1 to form t1 which is 1/3 from D to A. Fold A to t1 to form t2.
Fold A to t2 and crease to form s1 on BD. Crease Cs1 to form f1. f1 is 1/5 of AB. Fold A to s1 to create f3, A to f3 for f4 and f3 to f1 for f2.
With folds horizontal and vertical folds from each of the t1,t2,f1,f2,f3,&f4 we have 15 rectangles of the same size.
Part 2  displaying n/15's in part14/15  fold A towards o to form the line f3t2 (area of one 1/15 rectangle removed)
13/15  fold A towards o to form the line f1t2 (area of two 1/15 rectangles removed)

Posted by brianjn
on 20120725 21:58:43 